An algorithm for identifying the best current friend in a social network (2015)
A research field in the area of social networks (SNs) is the identification of some types of users and groups. To facilitate this process, a SN is usually represented by a graph. The centrality measures, which identify the most important vertices in a graph according to some criterion, are usual tools to analyze a graph. One of these measures is the PageRank (a measure originally designed to classify web pages). Informally, in the context of a SN, the PageRank of a user i represents the probability that another user of the SN is seeing the page of i after a considerable time of navigation in the SN. In this paper, we define a new type of user in a SN: the best current friend. The idea is to identify, among the friends of a user i, who is the friend k that would generate the highest decrease in the PageRank of i if k stops being his/her friend. This may be useful to identify the users/customers whose friendship/relationship should be a priority to keep. We provide formal definitions, algorithms and some experiments for this subject. Our experiments showed that the best current friend of a user is not necessarily the one who has the highest PageRank in the SN nor the one who has more friends.